Consider the following tables, Loan and Borrower, of a bank.
Query: \[ \pi_{\text{branch\_name}, \text{customer\_name}} (\text{Loan} \bowtie \text{Borrower}) \div \pi_{\text{branch\_name}}(\text{Loan}) \] where \( \bowtie \) denotes natural join. The number of tuples returned by the above relational algebra query is 1 (Answer in integer).
Consider the following tables, Loan and Borrower, of a bank.
Query: \[ \pi_{\text{branch\_name}, \text{customer\_name}} (\text{Loan} \bowtie \text{Borrower}) \div \pi_{\text{branch\_name}}(\text{Loan}) \] where \( \bowtie \) denotes natural join. The number of tuples returned by the above relational algebra query is 1 (Answer in integer).
Show Hint
Solution and Explanation
Step 1: Understanding the division operation.
The relational division operation finds the set of customers who have taken loans from all branches appearing in the Loan table.
Step 2: Extracting relevant data.
The distinct branch names from the Loan table are: Banjara Hills, Kondapur, SR Nagar, Balanagar. A customer must have taken loans from all these branches to be included in the result.
Step 3: Identifying customers who satisfy this condition.
By analyzing the Borrower table, we find that the customer Karteek has loans in Banjara Hills (L11), Kondapur (L14), SR Nagar (L22), and Balanagar (L23), satisfying the condition.
Thus, the number of tuples returned by the query is: 1
Top Questions on Relational Algebra
- Consider the following three relations:
Car (model, year, serial, color)
Make (maker, model)
Own (owner, serial)
A tuple in Car represents a specific car of a given model, made in a given year, with a serial number and a color. A tuple in Make specifies that a maker company makes cars of a certain model. A tuple in Own specifies that an owner owns the car with a given serial number. Keys are underlined; (owner, serial) together form key for Own. (\(\bowtie\) denotes natural join)
\[ \pi_{owner} \left( Own \bowtie \sigma_{color="red"} \left( Car \bowtie \sigma_{maker="ABC"} Make \right) \right) \] Which one of the following options describes what the above expression computes?- GATE DA - 2025
- Computer Science
- Relational Algebra
- Let us consider two relations HISTORY and SCIENCE as depicted in the following Tables 1 and 2 respectively:
Table 1: HISTORYSNo NAME CLASS 1 MOHAN 6A 2 SANJAY 6B 3 YOGESH 7A
Table 2: SCIENCESNo NAME CLASS 1 NARESH 6B 2 SANJAY 6B 3 YOGESH 7A
What is the output of HISTORY - SCIENCE?- CUET (UG) - 2023
- Computer Science
- Relational Algebra
- Which of the following statement(s) is/are true?
A. Selection operation yields horizontal subset of a relation.
B. Selection operation yields vertical subset of a relation.
C. Union operator can work on relation with different degree.
D. Intersection and Cartesian product operations are not binary.
E. A record is a column on a datasheet.- CUET (UG) - 2023
- Computer Science
- Relational Algebra
- Let us consider two relations Student and Major as shown in Table 1 and Table 2 respectively.
Table 1 : StudentTable 2 : MajorSr No. Name Course 1. Aman CS 2. Ravi ECO 3. Mohit HIS 4. Sanjay MATH How many Tuples will be in the result table after Student U Major operation.Sr.No Name Course 1. Sanjay MATH 2. Abhay ENG 3. Sita HINDI 4. Aman CS 5. Ravi ECO - CUET (UG) - 2023
- Computer Science
- Relational Algebra
Questions Asked in GATE DA exam
- Let \( p \) and \( q \) be any two propositions. Consider the following propositional statements.
S1: \( p \rightarrow q \), S2: \( \neg p \land q \), S3: \( \neg p \lor q \), S4: \( \neg p \lor \neg q \)
where \( \land \) denotes conjunction (AND operation), \( \lor \) denotes disjunction (OR operation), and \( \neg \) denotes negation (NOT operation).
(Note: \( \equiv \) denotes logical equivalence)
Which one of the following options is correct?- GATE DA - 2025
- Logic gates
In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of \( P \), \( Q \), and \( R \)?
- GATE DA - 2025
- Geometry
Consider designing a linear binary classifier \( f(x) = \text{sign}(w^T x + b), x \in \mathbb{R}^2 \) on the following training data:
Class-2: \( \left\{ \left( \begin{array}{c} 0 \\ 0 \end{array} \right) \right\} \)
Hard-margin support vector machine (SVM) formulation is solved to obtain \( w \) and \( b \). Which of the following options is/are correct?- GATE DA - 2025
- Vector identities
- Let \( X \) be a continuous random variable whose cumulative distribution function (CDF) \( F_X(x) \), for some \( t \), is given as follows:
\[ F_X(x) = \begin{cases} 0 & \text{if } x \leq t \\ \frac{x - t}{4 - t} & \text{if } t \leq x \leq 4 \\ 1 & \text{if } x \geq 4 \end{cases} \]
If the median of \( X \) is 3, then what is the value of \( t \)?- GATE DA - 2025
- Probability
- Consider a hash table of size 10 with indices \( \{0, 1, \dots, 9\} \), with the hash function \[ h(x) = 3x \, (\text{mod} \, 10), \] where linear probing is used to handle collisions. The hash table is initially empty and then the following sequence of keys is inserted into the hash table: 1, 4, 5, 6, 14, 15. The indices where the keys 14 and 15 are stored are, respectively:
- GATE DA - 2025
- Data Structures